Commercially, the cobalt catalysts introduced by Roelen, e.g., Co.sub.2 (CO).sub.8, are used at 150-180.degree. C./150-200 atm, conditions which lead to side-reactions, such as hydrogenation, isomerization and aldehyde condensation. In the so-called low pressure oxo process, rhodium complexes which are soluble in organic solvents, such as HRh(CO) (PPh.sub.3).sub.3, are used as catalysts, working at 90-110.degree. C./20 atm and thus yielding less undesirable side-products. This process as well as other homogeneously catalyzed hydroformylations are mainly used for the production of butyric aldehyde and other low-boiling aldehydes. However, with homologous or higher-boiling aldehydes, the distillative separation from the catalyst is problematic [G. W. Parshall, S. D. Itell, Homogeneous Catalysis, Wiley, New York, 1992]. For this reason, attempts are being made in the industry world-wide to perform hydroformylations in a two-phase system [B. Cornils, in New Syntheses with Carbon Monoxide (J. Falbe, ed.), Springer Publishers, New York, 1980; B. Cornils, E. Wiebus, Chemtech. 1995, 33]. To this end, water-soluble phosphanes, e.g., P(C.sub.6 H.sub.4 SO.sub.3 Na).sub.3, are used as ligands for the rhodium (TPPTS-Rh system). The Rh catalyst is present in the aqueous phase whereas the olefin and the product (aldehyde) are present in the organic phase. In this way, Hoechst/Rhone-Poulenc produce n-butyric aldehyde from propene [B. Cornils, E. Wiebus, Chem. Ing. Tech. 66 (1994), 916; W. A. Herrmann et al., J. Mol. Catal. 97 (1995), 65]. Unfortunately, this simple process is limited to ethylene and propene, which have a water solubility which, although low, is yet sufficiently high to be reacted in the aqueous or catalyst-containing phase. Homologous olefins, such as n-hexene or n-octene, are virtually not or but poorly reacted in this system. Therefore, there have been many attempts to solve this problem, e.g., using surfactants or phase-transfer catalysts, especially ligands or solvents, but only with limited success as recently reviewed by E. Monflier [Angew. Chem. 107 (1995), 2450; Tetrahedron Lett. 36 (1995), 9481]. An improvement is described by E. Monflier [supra] according to which .beta.-cyclodextrin derivatives (.beta.-CD derivatives) are added to the two-phase system, serving as solubilizers. In the case of longer-chain olefins, such as 1-octene or 1-decene, the activity of the catalyst system is increased thereby by a maximum of about 10fold so that reasonable yields of the corresponding aldehydes are obtained, i.e., with n/iso ratios of about 2:1. However, the chemical selectivity is only 85-90% as a rule, i.e., 10-15% of side-products is obtained. Internal (i.e., non-terminal) olefins, such as 5-decene, are virtually not hydroformylated at all (only 3% conversion), i.e., the catalyst system is not very active. In addition, a great disadvantage is the fact that a large excess of .beta.-cyclodextrin derivative is necessary; typically, the ratio of Rh:P(C.sub.6 H.sub.4 SO.sub.3 Na).sub.3 :.beta.-cyclodextrin derivative is about 1:8:14. The advantage of a moderate increase in activity by the use of CD derivatives is relativated in view of the disadvantages mentioned.